On rigidity and analytic inflexibility of surfaces of negative Gaussian curvature under a given direction of displacement of boundary points

Abstract

We study the infinitesimal bendings of first and second order of regular (classC2) surfaces of negative Gaussian curvature, which are bounded either a) by four asymptotic linesg1,g2,g 1 ′ , andg 2 ′ , or b) by two asymptotic linesg1 andg2 and a lineg which nowhere has asymptotic directions, under the assumption that connections are imposed on the surface permitting displacement of the points of the linesg1 andg2 (in the first case) and the lineg (in the second) in a constant direction.